You need to detect the end of each individual file, print your results for that file and reset the counts. See the explanation of eof(ARGV) in perlfunc:

#!C:\Perl
use strict;
BEGIN{
    @ARGV=map glob, @ARGV;
}
open(RES, ">>results.txt");
print RES "File Number    A    A%    B    B%    Null    Null%\n";
my $A = 0; #these three lines set my initial counts at zero
my $B = 0;
my $null = 0;
my $filenum = 0;

while( <> ){
    chomp($_);
    if ($_ eq "stringa"){
        $A++;}
    elsif ($_ eq "stringb"){
        $B++;}
    else {
        $null++;
    }
    if( eof( ARGV ) ) { ## true after the end of each individual file
        my $popa = sprintf( '%.2f', $A / 1000 ); 
        my $popb = sprintf( '%.2f', $B / 1000 );
        my $popnull = sprintf( '%.2f', $null / 1000 );
        my $filenum++;  #Add one to my filenumber

        print RES "$filenum        $A    $popa    $B    $popb    $null
+    $popnull\n"; 
        $A = $B = $null = 0; ## Reset counts for the next file
    }
}
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As I mentioned above, if OS/X is a *nix-like system, you probably don't need the @ARGV = map glob, @ARGV as the shell will take care of that for you. (Though it probably won't do any harm.)

Also, in your code you have several place where you do:

...
my $var = ....;
my $var = sprintf ... $var;
...
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If you are running with strict and warnings, you should be getting messages of the form: "my" variable $var masks earlier declaration in same scope at .......don't ignore them, they are there for a purpose.

I was about to post a reply with similar suggestions... Now the only new things I can add are
• on a Mac the

  BEGIN{
      @ARGV=map glob, @ARGV;
  }
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  is definitely not required.
• I also noticed that the OP is using #!C:\Perl as the shebang line. On a Mac this should be #!/usr/bin/perl for an Apple-supplied Perl, but will need a different path if it's a user-installed Perl (e.g., from MacPorts, or elsewhere)

I also noticed that the OP is using #!C:\Perl as the shebang line.

I missed that++. That's a very strange choice for someone using a MAC (which doesn't have drive letters?), and wouldn't work on any *nix variant I'm aware of.

---

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

#!C:\Perl
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perl path/file_name_of_script arg1 ...
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#!/usr/bin/perl
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path/file_name_of_script arg1 ...
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As for your question about iterating over a list of file names, a method that I find useful goes like this: the perl script expects as input a list of file names, loads those into an array, and then iterates over the array. At each iteration, if there's a problem with the file or its contents, issue a warning and skip on to the next file in the list; e.g.:

#!/usr/bin/perl

use strict;
use Getopt::Long;

my $Usage = "Usage: $0 [-p path] filename.list\n   or: ls [path] | $0 
+[-p path]\n";

my $path = '.';
die $Usage unless ( GetOptions( 'p=s' => \$path ) and -d $path );
die $Usage if (( @ARGV and !-f $ARGV[0] ) or ( @ARGV==0 and -t ));
    # need file name args or pipeline input

my @file_list = <>;  # read all input as a list of file names
chomp @file_list;   # get rid of line-feeds

for my $name ( @file_list ) {
    my $file = "$path/$name";
    if ( ! -f $file ) {
        warn "input value '$file' does not seem to be a data file; ski
+pped\n";
        next;
    }
    if ( ! open( I, "<", $file )) {
        warn "open failed for input file '$file'; skipped\n";
        next;
    }
    ...
}
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The exception to that rule is when the script is really intended for a specific task that always involves a specific location and/or filter for getting its list of file names to work on, because in that case, I'd rather not have to repeat the selection process on the command line every time I run the script.

I like BrowserUk's solution below, except that I'd probably rewrite it (I mostly didn't like the chained if-elsif's) in a manner similar to (untested:)

#/usr/bin/perl

use strict;
use warnings;
use 5.010;

BEGIN{ @ARGV=map glob, @ARGV }

print "File Number    A    A%    B    B%    Null    Null%";

my $default = '';  # set to something sensible, the empty string seems
+ good.
my @allowed = (qw/stringa stringb/, $default);
my (%count, $filenum);

while(<>) {
    chomp;
    $count{$_ ~~ @allowed ? $_ : $default}++;
    if (eof) {
        $filenum++; 
        say "$filenum       ", join '    ' =>
          map { my $x=$count{$_}; $x, sprintf('%.2f', $x/1000) } @allo
+wed;
        @count{@allowed}=(0) x @allowed;
    }
}

__END__
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I threw in some 5.10-isms in the course of doing so, but it wouldn't be terribly different with pre-5.10 exists.